The invention is directed to an apparatus for measuring the mass of a flowing medium wherein a temperature-dependent resistor is disposed axially of the flow. An apparatus is already known in which such a temperature-dependent resistor is disposed in a gap parallel to the flow, and a portion of the medium flows past this gap. However, there is the danger that particles contained in the medium will be deposited on the temperature-dependent resistor and cause an undesirable change in the characteristic curve in the apparatus for measuring the mass; in other words, incorrect measurement values will be produced.